Question 928821
<pre>Each arrangement is of the form

VCVCVC

where V stands for a vowel and C for a consonant.  We can choose
the three vowels {E,A,I} to go where the V's are in 3!=6 ways.

For each of those 6 ways to arrange the vowels where the V's are,
we can arrange the 3 consonants (D,T,L) to go where the C's are
also in 3!=6 ways.

So there are 6*6 or 36 ways.  

Edwin</pre>